So p' is not dp/dt it's dp/dv with c being the +C constant because capital costs are fixed directly into the end product (if materials cost 40 and you can make 40 units, that's exactly $1 per unit fixed cost, but if you can push workers to make 3/hr instead of 2/hr you've reduced your labor cost by 30%).
s' is defined as ds/dv where the rate of surplus is total surplus divided by wages.
So an increase in v will result in a decrease in both p' and s'.
And for clarity, the reason c is constant is because this process of surplus value extraction has already been applied to it. The fractional/raw materials are coming from another industry that has already extracted surplus and as a result turned the commodity into a store of use value and dead labor (profit). Something that can't have any more value extracted from it.
Yeah, most of Marx's formulas leave time out of the equation as all that you really need to understand the flow of capital generation of profit is the relations between capital, material, and wages.
If you read his examples though, time does come into play when dealing with time based pay (e.g. $20/week). But because time isn't in the base formulas, they still apply to wage relations that are per unit.
That being said, he did toy with the idea of time based labor vouchers and the concept of labor time. Something that is necessary as humans do live in a world where time progresses and time is a limited thing for all of us.
But when looking at profit, time only comes in as a secondary factor for reducing wages. E.g. getting people to make 3 widgets an hour instead of 2, which in the formula is represented as a change in s' because the share of C given out as v falls.
This is also what kick-starts the falling profit rate, as increasing worker productivity requires (in most cases) increases in the share of C given out as c (new machinery, training, better materials, etc.). Since profit is derived from v and not c, that means total profit can increase while rate of profit decreases. The total C goes up, but the share of v that makes it up decreases (while total v increases) which leads to decreasing rates of profit with increasing total profit.
To disambiguate:
p' == profit rate
s == surplus value
C = capital
c == constant Ccapital (maintenance, materials)
v = variable capital (Wages)
So p' is not
dp/dtit'sdp/dvwithcbeing the +C constant because capital costs are fixed directly into the end product (if materials cost 40 and you can make 40 units, that's exactly $1 per unit fixed cost, but if you can push workers to make 3/hr instead of 2/hr you've reduced your labor cost by 30%).s'is defined asds/dvwhere the rate of surplus is total surplus divided by wages.So an increase in
vwill result in a decrease in bothp'ands'.And for clarity, the reason
cis constant is because this process of surplus value extraction has already been applied to it. The fractional/raw materials are coming from another industry that has already extracted surplus and as a result turned the commodity into a store of use value and dead labor (profit). Something that can't have any more value extracted from it.ok thanks, i actually wondered if i had guessed wrong because i'm so used to time being the quantity that rate is relevant to.
Yeah, most of Marx's formulas leave time out of the equation as all that you really need to understand the
flow of capitalgeneration of profit is the relations between capital, material, and wages.If you read his examples though, time does come into play when dealing with time based pay (e.g. $20/week). But because time isn't in the base formulas, they still apply to wage relations that are per unit.
which makes sense, it wouldn't make sense to model what he wanted with time.
That being said, he did toy with the idea of time based labor vouchers and the concept of labor time. Something that is necessary as humans do live in a world where time progresses and time is a limited thing for all of us.
But when looking at profit, time only comes in as a secondary factor for reducing wages. E.g. getting people to make 3 widgets an hour instead of 2, which in the formula is represented as a change in
s'because the share ofCgiven out asvfalls.This is also what kick-starts the falling profit rate, as increasing worker productivity requires (in most cases) increases in the share of
Cgiven out asc(new machinery, training, better materials, etc.). Since profit is derived fromvand notc, that means total profit can increase while rate of profit decreases. The totalCgoes up, but the share ofvthat makes it up decreases (while totalvincreases) which leads to decreasing rates of profit with increasing total profit.